As mentioned above, terminals operating in a wireless network may exchange information via an intermediary device—e.g., a base station in the network. The exchange may be in the form of channel feedback for the communication channel or link (e.g., a Radio Frequency (RF) channel) (conveniently referred to herein as the “channel”) between the base station and the wireless terminals. The channel feedback may include, for example, one or more of (i) a Channel Quality Indicator (CQI) indicating channel quality of the wireless communication channel between the base station and a User Equipment (UE); (ii) a Precoding Matrix Indicator (PMI) indicating a preferred precoding matrix for shaping the transmit signal; and (iii) a Rank Indicator (RI) indicating the number of useful transmission layers for the data channel as preferred by the UE. The channel feedback may also include estimates of channel coefficients, referred to herein as Channel State Information (or CSI).
The channel feedback may enable the base station to adaptively configure a suitable transmission scheme to improve coverage or user data rate or to more accurately “predict” channel quality for future transmissions to the terminals. In case of a mobile communication environment of Third Generation (3G) and Fourth Generation (4G) cellular networks, such as Third Generation Partnership Project's (3GPP) LTE network, the Evolved Universal Terrestrial Radio Access (EUTRA) or Evolved Universal Terrestrial Radio Access Network (E-UTRAN) air interface for LTE may require a base station to allocate resource blocks to a UE or terminal where the resource blocks are generated by dividing the system bandwidth in the frequency domain. A base station may transmit wireless channel resource allocation information to a mobile handset, terminal or UE via a downlink control signal, such as the Physical Downlink Control Channel (PDCCH) signal in 3GPP's 3G and 4G networks. In modern cellular networks (e.g., LTE), after receiving this PDCCH downlink transmission (i.e., transmission from a base station to a mobile device), the UE may feed back the CSI via uplink signaling (i.e., transmission from a mobile device to the base station) to the base station such as the Physical Uplink Control Channel (PUCCH) or the Physical Uplink Shared Channel (PUSCH).
In “Completely Stale Transmitter Channel State Information is Still Very Useful,” by M. Maddah-Ali and D. Tse, Allerton Conference, 2010 (referred to hereinafter as “Paper-1”), a multi-user downlink Multiple Input Multiple Output (MIMO) scheme is described with a mechanism for information exchange between single-antenna terminals, wherein the terminals feed back CSI to the serving base station. The serving base station exploits this CSI to broadcast an additional signal, which each terminal uses to create a Virtual 2-antenna Receiver (V2RX). The benefit of the V2RX may include a boost in performance for each terminal, which can translate into better coverage, higher bit rate, higher cell throughput (e.g., in case of a cellular wireless network), etc.
FIG. 1 illustrates an exemplary arrangement 10 in which a base station 12 facilitates information exchange between two terminals 14, 15 to form a V2RX at each terminal. The base station 12 may have two transmit/receive antennas (not shown)—herein referred to as “antenna-1” and “antenna-2,” and may transmit information to two terminals (i.e., terminal A 14 and terminal B 15 in FIG. 1) operating in the wireless network served by the base station 12. The arrows 17 and 18 indicate such transmissions from the base station 12 to respective terminals 14-15. Each terminal 14-15 may have only a single receive antenna (RX antenna) and can communicate back with the base station 12, but cannot communicate directly with the other terminal (as indicated by an “X” mark on the dotted arrow 20). However, as discussed below, the terminals 14-15 may be able to exchange information with each other via the base station 12 as indicated by exemplary dotted arrows 22-23, which show, by way of an example, terminal B sending information to terminal A via base station 12 in FIG. 1. Similarly, although not shown by any dotted arrows in FIG. 1, terminal A may send information to terminal B via base station 12.
At time 1, the base station 12 may transmit symbols uA (via antenna-1) and vA (via antenna-2) intended for terminal A, which receives:yA[1]=hA.1[1]uA+hA.2[1]vA+zA[1]  (1)where hA.1[1] and hA.2[1] are antenna-specific channel responses associated with terminal A (i.e., channel responses from base station antenna-1 and antenna-2, respectively, to terminal A), and zA[1] is the channel noise associated with terminal A. As used herein, the term “symbol” may refer to information content transmitted by a single antenna in a single transmission from the base station 12 to one or more terminals over the communication channel between the base station and the terminal(s). In case of an LTE network, for example, such transmission may include a radio sub-frame, or transmission time interval (TTI), having one or more slots (not shown). Terminal A 14 can try to recover uA and vA from yA[1] using a method discussed below after equation (7). Being in the same communication environment, terminal B 15 is also “listening” to the transmission from the base station 12 to terminal A 14, and receives:yB[1]=hB.1[1]uA+hB.2[1]vA+zB[1]  (2)where hB.1[1], hB.2[1] and zB[1] relate to terminal B and are defined similarly to terminal A-related parameters mentioned above. If terminal A also had access to yB[1], it would use it along with yA[1] to form a 2-antenna receiver (V2RX), boosting its performance significantly. However, as mentioned earlier, terminal B cannot talk directly to terminal A (as symbolically represented by crossed-out dotted arrow 20). Thus, in the arrangement of FIG. 1, terminal B communicates indirectly with terminal A through the base station (as indicated by dotted arrows 22-23), allowing terminal A to form a Virtual 2-antenna Receiver (V2RX) as discussed below. Similarly, terminal A helps terminal B form its own virtual 2-antenna receiver. This process is explained below.
At time 2, the base station 12 may transmit symbols uB (via antenna-1) and vB (via antenna-2) intended for terminal B, which receives:yB[2]=hB.1[2]uB+hB.2[2]vB+zB[2]  (3)Here, terminal A 14 is also “listening” to base station's 12 transmission to terminal B 15, and receives:yA[2]=hA.1[2]uB+hA.2[2]vB+zA[2]  (4)where the channel responses (h[t]) and the noise terms (z[t]) are defined as above.
In the arrangement 10 in FIG. 1, before time 3, terminal B 15 feeds back estimates of antenna-specific parameters hB.1[1] and hB.2[1] to the base station 12. Similarly, before time 3, terminal A 14 also feeds back estimates of hA.1 [2] and hA.2[2]. The terminals A and B may provide these feedbacks via respective CSI reports to the base station 12. At time 3, the base station may form a new combined symbolwAB=hA.1[2]uB+hA.2[2]vB+hB.1[1]uA+hB.2[1]vA  (5)which it may transmit (to both terminals A and B) from antenna-1 only, for simplicity. It is noted here that wAB may contain very useful information for both terminals A and B, provided they are able to parse it out. Now focusing on terminal A, it is observed that terminal A receives:yA[3]=hA.1[3]wAB+zA[3]  (6)In response, terminal A can form a virtual second antenna signal using yA[3] (from equation (6) above) and yA[2] (from equation (4) above), suppressing the contributions of uB and vB. This virtual second antenna signal can be given by:
                                                                                          y                  A                  ′                                ⁡                                  [                  3                  ]                                            =                            ⁢                                                                    y                    A                                    ⁡                                      [                    3                    ]                                                  -                                                                            h                                              A                        ,                        1                                                              ⁡                                          [                      3                      ]                                                        ⁢                                                            y                      A                                        ⁡                                          [                      2                      ]                                                                                                                                              =                            ⁢                                                                                          h                                              A                        ,                        1                                                              ⁡                                          [                      3                      ]                                                        ⁢                                                            h                                              B                        ,                        1                                                              ⁡                                          [                      1                      ]                                                        ⁢                                      u                    A                                                  +                                                                            h                                              A                        ,                        1                                                              ⁡                                          [                      3                      ]                                                        ⁢                                                            h                                              B                        ,                        2                                                              ⁡                                          [                      1                      ]                                                        ⁢                                      v                    A                                                  +                                                                                                      ⁢                                                                    z                    A                                    ⁡                                      [                    3                    ]                                                  -                                                                            h                                              A                        ,                        1                                                              ⁡                                          [                      3                      ]                                                        ⁢                                                            z                      A                                        ⁡                                          [                      2                      ]                                                                                                                              (        7        )            Together, yA[1] and y′A[3] form a V2RX for terminal A. Thus, in effect, terminal A “sees” a 2×2 MIMO unicast scenario, and can use any appropriate method to recover uA and vA. In essence, with two observations yA[1] and y′A[3], terminal A has enough degrees of freedom to solve for the two unknown transmitted symbols uA and vA. This can be done through, for example, maximum likelihood detection, which jointly hypothesizes the values of uA and vA to find the most likely combination given the observation of yA[1] and y′A[3]. Another example is successive interference cancellation, in which symbol uA is detected first, treating the contribution from vA as interference. After detecting uA, the interference contributed by uA is then cancelled from yA[1] and y′A[3]. The cleaned-up signal is used to detect vA. The detection order of uA and vA may be reversed. FIG. 2 symbolically illustrates such 2×2 MIMO unicast scenario at terminal A with an “X” over the transmission 18 from base station 12 to terminal B 15 to indicate terminal A's suppression of contributory effect of uB and vB to form V2RX (as mentioned earlier). It is noted here that FIG. 2 is a symbolic illustration only; there is no suppression of actual transmission from base station 12 to terminal B.
Similarly, at time 3, terminal B receives:yB[3]=hB.1[3]wAB+zB[3]  (8)and combines it with yB[1] (from equation (2) above) to form a virtual second antenna for terminal B, suppressing the contributions of uA and vA. It is noted here that an equation similar to equation (7) can be obtained for terminal B as well, however such equation is not presented herein for the sake of brevity. As in case of terminal A, terminal B also “sees” a 2×2 MIMO unicast scenario and can recover uB and vB using an appropriate method as mentioned above. Like FIG. 2, FIG. 3 symbolically illustrates such 2×2 MIMO unicast scenario at terminal B with an “X” over the transmission 17 from base station 12 to terminal A 14 to indicate terminal B's suppression of contributory effect of uA and vA to form V2RX. It is noted here that FIG. 3 is a symbolic illustration only; there is no suppression of actual transmission from base station 12 to terminal A.
Overall, the communication scheme in the arrangement of FIG. 1 requires 3 channel uses (at times t=1, 2, 3) to transmit 4 symbols (uA, vA, uB, and vB). In that sense, there is a gain, which is identified as a gain in degrees of freedom in Paper-1.
The above-discussed V2RX creation scenario generalizes readily to a base station with M>2 antennas and M single-antenna terminals. The scenario also generalizes readily to terminals with N>1 receive antennas.